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Calculate the velocity of a satellite moving in a stable circular orbit about the Earth at a height of 2700 km?
Wiki User
∙ 14y ago
The answer to the question: What is the circular velocity of a satellite in meters whose orbit is 2700 km from the Earth surface?
Use Kepler's third Law
The answer is: 6623 m/s.
Formula used: (GM/d)^.5
G=6.67x10^-11m³/kg/s²
M=Mass of Earth=5.57x10^24kg
d=Distance of satellite from the Earth sea level plus radius of Earth=6378km
Bozidar kornic
Wiki User
∙ 14y ago
Wiki User
∙ 13y agoThe formula for orbital velocity is:
v = sqrt(((M^2)(G))/((m + M)(R))
When the mass of the orbiting object, m, is negligible compared to the mass of the larger object, M, which is true in this case, then the formula becomes:
v = sqrt((MG)/(R))
The variable R represents the distance between the center of gravity and the orbiting object which in this case is the radius of the Earth and the altitude of the orbiting object, which now makes our formula:
v = sqrt((MG)/(R + h))
So plug in values for G, R, and M and we get:
v = 7,626.555 m/s
Wiki User
∙ 14y agoThe moon's average distance from the earth is listed as 238,000 miles. Assume that its path is a circle with
this radius. The circumference of the circle is (pi D) = (2 pi R) = (476,000 pi) = 1,495,400 miles (rounded).
The moon completes one orbital revolution around the earth in 27.32 days.
Now we have a distance and a time ... everything we need to calculate a speed = (distance) divided by (time).
We just have to be careful about how we handle the units.
(1,495,400 miles / 27.32 days) x (1 day / 24 hours) = (1,495,400) / (27.32 x 24) (mile - day / day - hour)
= 2,280.68 miles per hour.
My TIME Almanac lists the moon's orbital velocity as 0.64 mile per second, which is 2,304 miles per hour.
So our calculation of 2,280.68 differs from the almanac's figure by only about 1% ! Not too shabby.
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